How Can We Deform a Material to Maximize Its Gravitational Field at a Point?

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To maximize the gravitational field at a specific point using a deformable material with mass and constant density, the shape of the material must be optimized so that every point on its surface contributes equally to the gravitational field strength. The discussion emphasizes that simply naming a shape is insufficient; a derivation of the shape's equation is necessary for a complete solution. Participants are encouraged to explore the mathematical principles behind gravitational fields and the implications of material deformation. The focus is on achieving a uniform contribution to the gravitational field strength from the surface of the material. Understanding these concepts is crucial for addressing the posed problem effectively.
ShayanJ
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Consider a piece of a deformable material with mass m and constant density \rho. To what shape should we deform it so that its gravitational field is maximum in a given point?
 
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This looks a bit like homework, so I'll start with a hint: for the best shape, every point on the surface will contribute the same to the gravitational field strength (I guess field strength is meant, not potential).
 
This isn't a homework, because I have no idea what to do about it!
I should say that just naming a shape isn't enough, the equation of the shape should be derived somehow!
 

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